1. Membrane Trafficking: a) Membrane wave: In collaboration with Dr. Min Wu from National University of Singapore, we established a mechanochemical feedback model that accounts for the ultrafast rhythmic propagation (>1micron/sec) of the endocytic machine on plasma membrane in immune cells. Following our previous model, we found that immune cells exhibit distinct rhythmic patterns on cortex depending on stimulation. These rhythmic propagations are ultrafast (>1&#956;m/sec), much faster than typical cellular traveling waves. Combining theory and experiment, we demonstrated that the feedback between membrane shape change and cortical protein dynamics (e.g., F-BAR domain proteins) drove their own oscillatory behaviors, rendering the cortex as an excitable system. Such excitability manifests itself as phase wave arising from the spatial gradient of cortical activation. Instead of real material propagation, it was this spatial gradient in the timings of the local oscillations that gave the propagating appearance, and it was the resulting phase velocity that dictated the ultrafast propagation speed. Interestingly, as the membrane topographic change accompanied such rhythm, it further fired up the cortical activation along the propagation path, potentiating wave propagation farther beyond the initial epicenter. This work uncovers the under-appreciated role of membrane shape in setting the spread rhythm of cortical activation signal. This paper is under review in PLoS Biology. 2. Cell Division: a) Spatial-temporal regulation of spindle assembly checkpoint: Faithful chromosome segregation in mitosis requires stable microtubule spindle attachment at the kinetochores (KT) of each chromosome. Until then the spindle assembly checkpoint (SAC) is active to prevent mitotic progression. However, the everlasting stochastic fluctuations and large KT number in the cell would deny robust timing of SAC silencing. From the stably attached KT, SAC components stream toward the spindle poles (SP). Incorporating the spatial-temporal regulation, we established a theoretical model that unprecedentedly accounted for the fidelity of SAC silencing. The poleward streaming from the attached KTs is integrated by the SP, yet diverted by the unattached KTs until the last KT-spindle attachment, causing a >2 fold jump in the SP accumulation. Such jump robustly triggers SAC silencing after and only after the last KT-spindle attachment. Our model explained intriguing observations on mitosis and offered a unified conceptual framework: Spatial-temporal regulation ensures the fidelity of SAC silencing. This paper is published in Nature Communications. b) The role of spindle pole organization in faithful mitotic exit: In previous work, we found that the spindle pole integrates the information from the kinetochores to govern the progression of mitosis, in particular the SAC silencing with regard to the last kinetochore-spindle attachment and thereby the correct timing for anaphase onset. In this study, we extended our model to incorporate the effects of supernumerary and the disorganization of spindle poles, which often manifest themselves in cancer cells. We found that fine-control over the number, the geometry and the size of spindle poles is the fundamental determinant for mitotic progression. Furthermore, the organization of the spindle poles must coordinate with the kinetochore tension for faithful anaphase onset. This result sheds light on the origin and the treatment of cancer cells. It puts diverse observations in cancer cell mitosis into perspective. The paper is submitted to Molecular Systems Biology. c) The mechanochemistry of low-copy-number plasmid segregation machinery The segregation of DNA prior to cell division is essential to the faithful inheritance of the genetic materials. In many bacteria, the segregation of the low-copy-number plasmids involves an active partition system composed of ParA ATPase and DNA-binding ParB protein, which stimulates the hydrolysis activity of ParA. Both in vivo and in vitro experiments show that ParA/ParB system can drive persistent movement in a directed fashion, just like a processive motor protein. However, the underlying mechanism remains unknown. We have developed the first theoretical model on ParA/ParB-mediated motility. We establish that the coupling between the ParA/ParB biochemistry and its mechanical action works as a robust engine. It powers the directed movement of plasmids, buffering against diffusive motion. Our work thus sheds light on a new emergent phenomenon, in which elaborate mechanochemical couplings of non-motor proteins can work collectively to propel cargos to designated locations, an ingenious way shaped by evolution to cope with the lack of processive motor proteins in bacteria. This paper is submitted to PNAS. 3. Cell Motility: a) Mechanochemistry of focal adhesion formation: Durotaxis cells prefer to migrate toward stiffer substrate is important for many physiological processes. Focal adhesion (FA) is a dynamically formed organelle, serving as the foot of migrating cells. To better understand the mechanosensation underlying durotaxis, we provided the first theoretical model that integrates the contributions of branched actin network and stress fiber in the FA formation. It captured the salient features of FA growth in coupling with the cell leading edge protrusion. The model predicted two traction force peaks emerging within the growing FA: While the distal traction peak originates from the catch bonds that mediate FA-retrograde actin flux engagement, the central one is generated by the actomyosin contractility from stress fiber. The centraal traction peak oscillation due to the stress fiber-mediated negative feedback optimizes the range of FA mechanosensing on substrate stiffness. The competition between the two sources of tractions gives rise to the traction peak oscillation within single FAs. We experimentally perturbed the two types of actin networks, and convincingly verified these unique model predictions. Our study thereby established the coherent picture of FA formation. FA is truly a mechanosensory organelle: Its traction force generation is part of the FA-intrinsic regulatory feedbacks, which consolidate the dynamics of branched actin network and stress fiber to precisely measure up the substrate stiffness in the physiological range. Our work thus sheds light on the mechanistic nature of durotaxis. This paper is in collaboration with Dr. Clare Waterman's lab, and is under 2nd round revision for PNAS.